Yes, the temperature of a material is in fact the random movements of molecules. The kinetic energy (hence the velocity) of the molecules is n/2·kT where n is the freedom degrees (1 of a signe atom, more for multiatomic molecules, depending on their shape), k is the Bolzman constant 1.38044 E-23 J/Kand T the absolute temperature.

İ would suggest changing the term "heat" to "thermal energy" in your question text.